Smoothen a Gravelly Concrete Patio

Hi all,

I have an old house with a back patio of poured concrete with gravel on top. The previous owner carved/left a box within the patio to plant a crepe myrtle and hostas within 4 ft of the house. While the myrtle is quite beautiful when it blooms, the flowers become a nuisance when they fall onto the patio and get stuck/decompose within the nooks of the gravel. Short of cutting down the tree, I'd like to smoothen the patio so that it can be easily swept. Can I just pour additional concrete and even out the surface? Or is it more complicated than that?